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Spectral Theory of Infinite-area Hyperbolic Surfacesby David Borthwick
Springer 2007; US$ 79.95By focusing on the scattering theory of hyperbolic surfaces, this work provides an introduction to the geometry of hyperbolic surfaces. Aimed at graduate students and researchers, it draws on techniques from functional analysis and differential geometry, as well as some techniques from algebra and number theory. more...
Geometry of Riemann Surfaces and Teichmuller Spacesby M. Seppälä; T. Sorvali
Elsevier 1991; US$ 225.00The moduli problem is to describe the structure of the space of isomorphism classes of Riemann surfaces of a given topological type. This space is known as the moduli space and has been at the center of pure mathematics for more than a hundred years. In spite of its age, this field still attracts a lot of attention, the smooth compact Riemann surfaces being simply complex projective algebraic curves. Therefore the moduli space of compact Riemann surfaces is also the moduli space of complex algebraic curves. This space lies on the intersection of many fields of mathematics and may be studied from many different points of view. The aim of this monograph is to present information about the structure of the moduli space using as concrete and... more...
Dynamik meromorpher Funktionen auf der Riemannschen Zahlenkugelby Christoph Dötsch
Diplomica Verlag 2008; US$ 51.48Hauptbeschreibung Fatou und Julia veröffentlichten 1919/1920 bzw. 1918 ihre berühmten Arbeiten über die Iteration komplexer rationaler Funktionen. Durch die Anwendung des Konzeptes der normalen Familie durch Fatou und Julia standen der komplexen Dynamik nun funktionentheoretische Ergebnisse zur Verfügung. Julia und Fatou gelang so der Durchbruch bei der Betrachtung des globalen dynamischen Verhaltens der Orbits: Sie stellten fest, dass die Riemannsche Zahlenkugel in zwei disjunkte Mengen zerfällt. In die heutzutage als Fatou - Menge bezeichnete Menge F(R), auf der zwei Orbits ein ähnliches Verhalten aufweisen, wenn ihre Startwerte hinreichend nahe beieinander liegen. Und in die heutzutage als Julia - Menge bezeichnete Menge J(R), auf der... more...
Generalizations of Thomae's Formula for Zn Curvesby Hershel M. Farkas; Shaul Zemel
Springer 2011; US$ 124.00Previous publications on the generalization of the Thomae formulae to Zn curves have emphasized the theory's implications in mathematical physics and depended heavily on applied mathematical techniques. This book redevelops these previous results demonstrating how they can be derived directly from the basic properties of theta functions as functions on compact Riemann surfaces. "Generalizations of Thomae's Formula for Zn Curves" includes several refocused proofs developed in a generalized context that is more accessible to researchers in related mathematical fields such as algebraic geometry, complex analysis, and number theory. This book is intended for mathematicians with an interest in complex analysis, algebraic geometry... more...
Topics on Riemann Surfaces and Fuchsian Groupsby E. Bujalance; A. F. Costa; E. Martínez
Cambridge University Press 2001; US$ 86.00Introduction to Riemann surfaces for graduates and researchers, giving refreshingly new insights into the subject. more...
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